{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "S+P Week 1 Lesson 2.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w_XJiOdr-MSM",
        "colab_type": "text"
      },
      "source": [
        "# Lesson 2\n",
        "\n",
        "In the screencast for this lesson I go through a few scenarios for time series. This notebook contains the code for that with a few little extras! :)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "vidayERjaO5q"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "XpzEXzbHoQhj",
        "colab": {}
      },
      "source": [
        "!pip install -U tf-nightly-2.0-preview"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gqWabzlJ63nL",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "sJwA96JU00pW",
        "colab": {}
      },
      "source": [
        "def plot_series(time, series, format=\"-\", start=0, end=None, label=None):\n",
        "    plt.plot(time[start:end], series[start:end], format, label=label)\n",
        "    plt.xlabel(\"Time\")\n",
        "    plt.ylabel(\"Value\")\n",
        "    if label:\n",
        "        plt.legend(fontsize=14)\n",
        "    plt.grid(True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "yVo6CcpRaW7u"
      },
      "source": [
        "# Trend and Seasonality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "t30Ts2KjiOIY",
        "colab": {}
      },
      "source": [
        "def trend(time, slope=0):\n",
        "    return slope * time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "iJjc3G1Maefn"
      },
      "source": [
        "Let's create a time series that just trends upward:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BLt-pLiZ0nfB",
        "colab": {}
      },
      "source": [
        "time = np.arange(4 * 365 + 1)\n",
        "baseline = 10\n",
        "series = trend(time, 0.1)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "WKD4nh9sauBf"
      },
      "source": [
        "Now let's generate a time series with a seasonal pattern:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "89gdEnPY1Niy",
        "colab": {}
      },
      "source": [
        "def seasonal_pattern(season_time):\n",
        "    \"\"\"Just an arbitrary pattern, you can change it if you wish\"\"\"\n",
        "    return np.where(season_time < 0.4,\n",
        "                    np.cos(season_time * 2 * np.pi),\n",
        "                    1 / np.exp(3 * season_time))\n",
        "\n",
        "def seasonality(time, period, amplitude=1, phase=0):\n",
        "    \"\"\"Repeats the same pattern at each period\"\"\"\n",
        "    season_time = ((time + phase) % period) / period\n",
        "    return amplitude * seasonal_pattern(season_time)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "7kaNezUk1S9l",
        "colab": {}
      },
      "source": [
        "baseline = 10\n",
        "amplitude = 40\n",
        "series = seasonality(time, period=365, amplitude=amplitude)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "-Vo433h0bDLD"
      },
      "source": [
        "Now let's create a time series with both trend and seasonality:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AyqFdaIN1oy5",
        "colab": {}
      },
      "source": [
        "slope = 0.05\n",
        "series = baseline + trend(time, slope) + seasonality(time, period=365, amplitude=amplitude)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YVdJ2jNN8OHk",
        "colab_type": "text"
      },
      "source": [
        "# Noise"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "V4taP424sces"
      },
      "source": [
        "In practice few real-life time series have such a smooth signal. They usually have some noise, and the signal-to-noise ratio can sometimes be very low. Let's generate some white noise:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "3kD3_zjVscBH",
        "colab": {}
      },
      "source": [
        "def white_noise(time, noise_level=1, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    return rnd.randn(len(time)) * noise_level"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "aLvBwrKrtDzo",
        "colab": {}
      },
      "source": [
        "noise_level = 5\n",
        "noise = white_noise(time, noise_level, seed=42)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, noise)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "GHa6gicgbL74"
      },
      "source": [
        "Now let's add this white noise to the time series:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "2bRDx8K816N9",
        "colab": {}
      },
      "source": [
        "series += noise\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "a1sQpPjhtj0G"
      },
      "source": [
        "All right, this looks realistic enough for now. Let's try to forecast it. We will split it into two periods: the training period and the validation period (in many cases, you would also want to have a test period). The split will be at time step 1000."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "_w0eKap5uFNP",
        "colab": {}
      },
      "source": [
        "split_time = 1000\n",
        "time_train = time[:split_time]\n",
        "x_train = series[:split_time]\n",
        "time_valid = time[split_time:]\n",
        "x_valid = series[split_time:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "GICxGswL2aqK",
        "colab": {}
      },
      "source": [
        "def autocorrelation(time, amplitude, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    φ1 = 0.5\n",
        "    φ2 = -0.1\n",
        "    ar = rnd.randn(len(time) + 50)\n",
        "    ar[:50] = 100\n",
        "    for step in range(50, len(time) + 50):\n",
        "        ar[step] += φ1 * ar[step - 50]\n",
        "        ar[step] += φ2 * ar[step - 33]\n",
        "    return ar[50:] * amplitude"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "mCaWIWoDGVCL",
        "colab": {}
      },
      "source": [
        "def autocorrelation(time, amplitude, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    φ = 0.8\n",
        "    ar = rnd.randn(len(time) + 1)\n",
        "    for step in range(1, len(time) + 1):\n",
        "        ar[step] += φ * ar[step - 1]\n",
        "    return ar[1:] * amplitude"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "MVM204K66bnC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "7c6884b9-87ce-43a8-f0d1-7122a944f148"
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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1GvOy45ZGUQf1ZLLPbOxAyEY9RUP8ij2nixlRPALgwwBOEkKOmY/9ewB/BuA5QshvArgK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\nUUWhKIqiVOT/ASBOYvr9FZaAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "9MZ2sCmM8XPU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "2f97dc15-0252-46dd-82b5-90837d4d2db6"
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + trend(time, 2)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xvdbXGWOiRGQ98Jg1lzUishF4wBiz57Tj3YXjEhQJCQkZ69YNKVf1aG5uJiws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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "hqx5et9Bzp5e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "f705dc4d-5e6a-4b0e-83df-94e112414259"
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
        "plot_series(time[:200], series[:200])\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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U/QF4A8gzHu8Dvh6EczuBf9ValwHnA3crpcqA+4C3tdZTgLeNxwBXAlOM2wrg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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "qb5echI7rHqA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "0695d1b3-2947-4d44-d1c0-2d2cf997e9d5"
      },
      "source": [
        "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
        "series2 = autocorrelation(time, 5, seed=42) + seasonality(time, period=50, amplitude=2) + trend(time, -1) + 550\n",
        "series[200:] = series2[200:]\n",
        "#series += noise(time, 30)\n",
        "plot_series(time[:300], series[:300])\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QdRtP7TrDJTPTKMpO4I1jDTywsZzWbgfp8dG8+e1rJzyNEkBE2HC4NP4sobGs\nMAW3hgNVbVwyM83ncU738OuLhIO8fsuyhnM+xPCUUvzy9qUsyE3iJy8c5qtP7eGVQ7V09bl45p1K\nLErR0etknjkA9vsbDvLywVqSJjhd8ombgpr9HKkdapzukceBAN5BfHvONNPV5/SZV396YYW6/gEk\nnPMhRqaU4tNXzuKeq2axfk81WsPfPnMpTrdGKfjnV67kxS9fyZ0rpjMtLY6/nDeDwkSQEsgU8+dt\nFXx3/UF+8+ELeffSvGAnZ1ScLo3Vj09sRkIMBamxvHqojp++eIQfvmchd182Y9BxI61wGA7S46OJ\ntlnoc8pAwqnimzfOxx5lZX5OIpfNzuBPH7+Y+Bibd0lnzzEAuvHIhKZFPnFTSFltO99dfxCAfZWh\nP0jpfA4/SyBglEJ2mCPG/3ng7JDHeNdYD+O2A6UUeeY4ASmBTA0Wi+Lfrp/LTWab3GVzMgZNnXPL\nklxuWZI7bjM/+0zLhJ5dhJQNe6uxmIOdPLPJhhOnS2Pz8wtxYb8vlKd75PkcfvbCCnWeaqxwDoQi\nPEkV1hShteb5fTWsnJ1OXLSNkw2dwU7SqDn8mI3Xo/8vsqqW7iGP8bSBhPv4CU8ACeeqOBGe5BM3\nRZxqc3OyoZN3L8ljVkY8FY1duNzh1ZDubyM6wJKCZK5fkM2SgmSfq8Y5/BiJHg6kCksES3h/c8SI\ntNaUHq1jS5UTm0Vx46IcZmbE0+d0U+3jl3mo8mc9EI8Ym5U/3FXMTYtyae5yeBd96s8RAb2woH8V\nlnydxeSST1yEK6/r4OOP7uTV006uLMogJS7aO5L6RJhVYzlc7lFP41CQatxchyqFRMI4EOhXhRXm\ngVCEn/D+5ogR9V9Y6baLCgFjzW4wemWFE6fb/xKIR6E5vUdl0+DSlnOUI9FDlWc0upRAxGSTT1yE\n88z3tGZJDLcsMbr9pSfEkJ8Sy97KkSccDBVaa1wBBBBPCWSoXmfecSBh3gurIDWO9Phob16FmCzS\nCyvCeer5U2MG3nmXFiazNwwWrPHw5GO0P7LT46NJiYuibIi1q71L2o60yEiIs0dZ2fGd60JqllYx\nNYT3Ty8xIk89//k33qUFKZxu6qLpvDUuQpUnH6O91yulmJedyNGzbYPPGSHjQAAJHiIowv+bI4bl\nqec/v+pnSYExTmJvmIxIP1cCGf2Ncl5OIsdqOwbNieWIkHEgQgSLBJAI56nnHxxAkom2Wdh0tD4I\nqRo9p498+GNeTiIdvc5BAwq9pRppfBYiIPLNiXCeev7zf7nHx9hYNT+L5/fVeG/Oo3Wstp2KSeoK\n7M1HAAFkfk4iAEfPDux1FimXBY/5AAAgAElEQVTjQIQIFgkgEc5XCQRg9bI8Gjp6eaO8IaBz33D/\nZkp+UTqG1PnPm48APrFF2WYAOa/b8rmpTORrIEQg5JsT4c6teTF4X8m8LPJTYvn++oO09Tj8PqfL\nrTnb2jNeSfSLr7YcfyTZo8hMjBlUWnK63SglDdBCBGrEAKKUylZKrVVKvWQ+X6CU+tRY31gpVaiU\n2qiUOqSUOqiU+rK5PU0p9YpSqsz8N9XcrpRSv1ZKlSul9imllo81DVOBtxfWEPdIe5SVX394Gaeb\nunhyxxm/z/n+373Jiv98bbySyDunm/nWM/uGnZvrXG+ywG72MzPiB00g6XDpsB8DIkQw+fPt+RPw\nMuBZfegY8JVxeG8n8DWt9QJgBfAFpdQC4FvAa1rrIuA18znATUCR+bcG+N04pCHiOUb45X7R9DTS\n46NHNa3J+eNH3GOclPGxNytYt/MMO042+TxmpHyMZNYQAcTpcof9KHQhgsmfAJKhtX4KcANorZ2A\na/iXjExrXaO1fsd83A4cBvKB1cBj5mGPAe81H68GHteGt4AUpVTuWNMR6by9l4b55V6QFseZUawP\nkpkYM+B5a7f/1V/nc7s1b5QZbTDP76v2edxwVXH+mJERT0NH34CqOqdbSwO6EGPgz0j0TqVUOqAB\nlFIrgHGdA0MpNQO4ENgOZGuta8xdZ4Fs83E+0L+epdLcVtNvG0qpNRglFLKzsyktLQ04XR0dHWN6\nfSg4ctK4YfZ0dfrMi93Rw7FGt995dTv6mJtqYXmWjXVH+3hp4xbyEgK7s1e0umjq7CPOBhveOc0l\ncQ0k9xs1f7rNxTNlDsqajd8sfT09AV2TzlpjNt5nXt7MzGQrAKfO9KLdzqBd40j4fHlIXkLTROfF\nnwDyVWADMFsptRXIBG4brwQopRKAZ4CvaK3b+i/BqLXWSqlR1Y9orR8GHgYoLi7WJSUlAaettLSU\nsbw+FByiHI4eJTkx3mdedvQc4e3NJ7jiyqv8GhMR9eZrLJ+TyXuW5rHu6HZmXrCUlbPTR5228rp2\nfv7EHpTq4VcfKebeJ3bzi72axz95ibfN4iu/3YrLpegyZ2NPiIsN6Jrk17bzm92bSZs+n5Jl+QC8\n1LCPuNa6oF3jSPh8eUheQtNE52XEu4VZzXQ1cBlwD7BQa71vPN5cKRWFETz+qrX+h7m51lM1Zf5b\nZ26vAgr7vbzA3CaG4U/vpWlpcTjdmho/e1Y53RqrRZGeYFRlNXb2+jx2/Z4qfvz8oQHb1m45yQcf\n2sb3NxykuqWbBz+ynOsXZLNuzQq6el3c/tA2OnudPPB6Ob0ON+u/eLn3tYH2uJ2WbszKW9FwrqrO\n4XZHxDQmQgSLP72w7gI+AlwELAc+bG4bE2UUNdYCh7XW/9Nv1wbgbvPx3cD6ftvvMntjrQBa+1V1\nCR88bSDDVfV7pjw/42PlvkHndLuxWRTpCdEA/Oi5Q3zwoW08ufP0oGO/vG4Pa7ecZPfpZgAOVLXy\nny8eZkdFE1vLG/n4ZTO4ebHRlLW0MIVf3L6Uho5e/nXoLM/treb24gJmZSbgKZgG2uYdY7OSGhdF\nfce5IOl0aZnGRIgx8KcK6+J+j+3AKuAd4PExvvflwJ3AfqXUHnPbfwA/A54yuwqfAj5o7nsRuBko\nB7qAT4zx/acEh9u4SfavGjzfNE8AaeqC2SOf0+XSWC0WUuOMAFLX3kt7j5Ndp5po7nJw8YxULpqe\nBkBijI32Xie/LT3OH+4q5tGtFcRFW1lamMJbJxr5yKXTBpy7eEYqSsF9Lxymz+XmE5fPBOCiaans\nOtVM3xi6b2Ql2qlrO1dacrrdMo2JEGMwYgDRWn+p/3OlVAqwbqxvrLXeAvi6q60a4ngNfGGs7zvV\nOF0jV9PkJtuJsioqGv0tgRhBqX/Prvs/tIz7XjzEz146woz0OEr//Rpaux209zqJsipePVxLTWs3\nb59q4tJZ6fzyg0s53dhFdpJ9wLkT7VHMy07kyNl2iqenMjMj/tz5XzjM7JTBs+r6Kysphrr2cwHE\n4ZJeWEKMRSA/vzqBmeOdEDExHC494lgHm9XCtLQ4TtQPXjNjKC6zDaS/VRdk8ffPXsaVRRlUNnfj\ncmvKzTU4vn3TBWgNv990gorGLoqnp5Jkj2JRfvKQ579oeipgTLXiUZgWx0N3XoR9DGt3ZCbEUN8v\ngDhdbpnGRIgxGLEEopR6DrMLL0bAWQA8NZGJEuPH6fbvJjk7M4Hj9f4NJnSYbSAAP1q9EKtFEWW1\nkJ1k5+bFubxR1kBNazfHzQCy6oIsXj54lj+9WQEY1VTDedfCHDYdq+eWJXnDHjdamUlGANFao5Qy\nxoFIG4gQAfOnDeQX/R47gVNa68oJSo8YZ04/q2lmZyWw8WidOTrbd8BxuzVag9WsFrtr5YwB+6eb\nvZ1ONXZRVtdOjM1CQWoc/3HzBax+cCuAz5KHx1VzM9nyzWtHTPNoZSXa6XO5ae12kBIXjcPllqlM\nhBgDf9pANk1GQkLV6cYuclPsYVvV4XBpv9I+KyMeh0tzprnb2+4wFM+06r5+uc9IN157sqGTTcfq\nWZSfjNWiWFqYwsavl3C2tYcYmzWAnIxdljmCvq69l5S4aJwuTXSgQ9uFEL7bQJRS7UqptiH+2pVS\ngbdkhpGOPs1192/i0a0ng52UgBk9jfwrgQDeaidfPBMe+irV5CTZibZZeG5vNcdqO/jA8gLvvpkZ\n8QENOBwvnilYPO0gRg81CSBCBMrnt0drnai1ThriL1FrnTSZiQyWY80u+pxuNh0Lj1X7huJ3FVaG\nGUBGaEh3jDArrsWiSI2LYvvJJuxRFm5dGjrTlZ0rgRhjQYxGdGkDESJQfv/8UkplKaWmef4mMlGh\n4lizcbPcVdFMj2PM80cGhcPPnkbJcVEkxthGHI3u8mMVvxWzjFLG925dSJI9ahSpnVhZZpfhg1VG\nAdoIrlICESJQ/vTCeg/wS4zp3OuA6Rgz5y6c2KQFX1mzi2ibhV6nm92nW4Ja/RKo0fQ0yk62j7hQ\nlHdp2WGC0k/eu4jvv3shafHR/id0EiTE2LhhQTZ/3HKSOVkJRm8yKYEIETB/fn79GGO9jmNa65kY\ng/zemtBUhYD2HgcVbW5uu6gAi4JtJxqDnaSAOPwYSOiRk2Sntn2EEogZQKKGKYEk2qNCLnh4/Paj\ny1lamMLDm0/Q55RxIEKMhT/fHofWuhGwKKUsWuuNQPEEpyvo/m93FS4Nt19UwOL8ZLYdb2BXRRMt\nXX3BTtqojGa+p6ykGGpHKIE4/FhfJJTZrBbuXDGdEw2dVDZ3y0h0IcbAnwDSYk65/gbwV6XUrzBG\no0csrTWPbzvFjCQLywpTWDk7g3dOt3D777dx3wuHg528UfF3ICEYJZC69t5hVxh0jdCNNxzcuiSX\nJLtReytzYQkRuOG68T6olLoCYyXALoxlbP8JHAfePTnJC45TjV1Ut3SzapoNpRQrZ6fjMgfQPbev\nesCqdqHOmMrEzwCSbMfp1jR2+i5ledtAwrjx2R5l5f1m92LphSVE4Ia7CxwD/hs4iDFD7mKt9WNa\n61+bVVoRa0ZGPG/9xypW5Bm/Ui+ekUpijI1r52fR43CzYY/vpVdDjdPtHra9or+sRKOXUm2b72os\nf9pAwsGHLzE6EkovLCECN9w4kF9prVdiLCbVCDyilDqilPqeUmrupKUwSBLtUd6bZFy0jc3fuIY/\n3lVMRkI0B6rGdUXfCeVw+t8LKyfZCCDD9cQK9zYQj3k5ify/Wy7gfRfmBzspQoQtf1YkPKW1/rnW\n+kLgw8D7MLrxTimp8dFYLIrCtDhON/k37XkocIxizYscc5zEcD2xIqENxOPTV85iccHw83IJIXzz\nZ0VCm1Lq3UqpvwIvAUeB9094ykJUYWqc3yv3hQKnS/td3ZSREI1FMWxPrEhoAxFCjI/hGtGvV0o9\nAlQCnwFeAGZrre/QWq/39bpIV5gWS3VLj3ep2FA30uy6/dmsFjISYqht873GeaS0gQghxm64kejf\nBv4GfE1r3TxJ6Ql5halxuNyamtYe71riocyzpK2/cpLtnB2mEd0ZIW0gQoix8xlAtNbjvyBDBPCu\nH97cFRYBxJ8lbfvLSrRTOUwV3UjTuQshpg6pyB4lT9A4EyYN6U4/lrTtLyc5xq9uvNIGIoSQu8Ao\n5SbbsVoUFY3hEUAcoxiJDkZPrOYuh8/Zh50jrAcihJg6JICMks1qYUFuEm+fCo9mIX/XA/HwTHle\n56Mh3dMGIlVYQggJIAFYOTudPadbQn6NEK21OZ376Eog4HssiJRAhBAeEkACsHJWOn0ud8iXQpwB\ndLkdaTS6tIEIITzkLhCAi2emYbUotof4GiFOz+qBoyiBZI8wH5aUQIQQHhJAApAQY6MwNZYTDaE9\nq71n/fLRjANJirWRHh/Na4fr0HrwtO7SBiKE8JAAEqCC1Dgqm7uDnYxheUogo+mFpZTiK9cVse1E\nI78tPT5oxP25qUwkgAgx1QU1gCilHlFK1SmlDvTblqaUekUpVWb+m2puV0qpXyulypVS+5RSy4OX\ncihIjQ2DABJYaeEjl07nmnmZ/PfLR/lt6fEB+7yTKUobiBBTXrDvAn8Cbjxv27eA17TWRcBr5nOA\nm4Ai828N8LtJSuOQClJjaejoDemeWA5vI/roLrPVonjk4xczPyeRd04P7CggJRAhhEdQA4jWejPQ\ndN7m1cBj5uPHgPf22/64NrwFpCilcicnpYMVpBoj0kO1FFLb1jOm9gqlFLOzEjhRP7Cdx3NOWclP\nCDHcZIrBkq21rjEfnwWyzcf5wJl+x1Wa22r6bUMptQajhEJ2djalpaUBJ6Sjo8Pn6+ubjZLHi5ve\nYklmaP037jzr5ME9vdy5IBqAY0ePsCixZ9T/F9bOPs40OXjl9Y3ersBlx43lbrdueSMoM/IOd03C\njeQlNEle/Bdad77zaK21UmpwV6DhX/Mw8DBAcXGxLikpCfj9S0tL8fX6+a093Lf9NdIKiyhZMT3g\n95gI9z+4FeilNSoDqGbpooXENh71mRdfWlOq2HB8D9MXFjM3OxGAfa4yKDvGtSUlQanGGu6ahBvJ\nS2iSvPgv2G0gQ6n1VE2Z/9aZ26uAwn7HFZjbgiIrMYYoqwq5KqwzTV3sq2wB4FBNGzC6cSD9zcpI\nAOB4XYd3m6cNRJpAhBChGEA2AHebj+8G1vfbfpfZG2sF0NqvqmvSWSyK/JTYYac+D4Zdp5rQGvJT\nYik3b/xFWQkBnWtmZjzAgPEuxvTwCqUkgggx1QW7G+8TwDZgnlKqUin1KeBnwPVKqTLgOvM5wIvA\nCaAc+APw+SAkeYCJGAuy7Xgjd67dzvfWH+C5vdWsfmDLkKsfut2ax7dVcOtv3uDuR3bQ3uMA4Fht\nB1FWxc2LcwCYn5PIjIz4gNKSEGNjRnocm47Ve7e53KObHl4IEbmC2gaitf6wj12rhjhWA1+Y2BSN\nTkFqLK8erhv5wFF4dnclb5Q18EZZA9uON1JW18HB6jaWFqYMOO7RNyv48fOHKMpKYNOxeraWN3Dj\nolzKatuZmRHP4gLj+BsW5owpPR+5dBo/ffEIB6tbWZiXbEzOKGNAhBCEZhVW2JiIsSBVLd2kxkUB\nUGZWQT269SQ/fO4gbrP9ob3HwQOvl3FlUQbP33sFMTYL2082eV9TlJXIZbPTuXxOOrdfVDCm9Hyo\neBqxUVae3Gl0gHO5tYwBEUIAEkDGZCLGglQ1d3PZnAwK02K92/5vTzWPbq2gqsV4n+f21tDc5eCr\n188lxmZl+bRUdlY00d3n4nRTF0XZCWQkxPDXT68Y87K7yXFRLJ+ewu7TRsO8w2wDEUIICSBjUJBq\n3OT9bUjvdbq8bRVDcbs11S09FKTEcvXcTCwK3rUw27u/rK4dgN2nm0mLj2aZWa11ycw0DlW38fe3\nz6A13i6342VxfgpHzrbR63RJG4gQwksCyBh4SiBn/CiBVLV0s+B7L/OJR3f6PKaho5c+l5uC1Fi+\nvGouj3/yUu5dVcSHio3ey2W1RpXW3soWlhQke3tC3bw4lxible+uP0hBaiwrZqWPNWsDLC1IxuHS\nHK5plzYQIYRXSA8kDHXesSBNI5dAfvrCYVxuza5TzXT1OYmLHvxfX2lWUeWnxpKZGENmYgwAP79t\nCRuP1lFW10FHr5Oyug5uWnRuFpd5OYls/sY1bD/ZyDXzsoiPGd/LusQs6eyvbJE2ECGEl/yUHAOL\nRTEjPd473mI4TZ193sd7z7TS1eekubOPY7XtPL+vGq21ty0lP2Vwu0VRdgJldR0cqGpFa7zVVx6Z\niTHcuiRv3IMHQF6ynbT4aA5UtUkbiBDCS0ogY7QwL4m3Tpw/H+RgTrebBblJHKpp453Tzfx+83Eq\nGjqxR1k5cradHyQcoqGjFzBKIOcrykrk6V1n2GH2tjq/W+9EUkoxIz2OM81dJMdGSRuIEAKQEsiY\nLcpP5mxbD/XtvcMe53Rr0hOimZUZz7qdpyk9Wk9FYxdHzhoN47Mz48lPiWVWZjwJQ5QiFuUn09nn\n4vFtFSwtSCYtPnoisuOTZ9Ck061lPXQhBCABZMwW5iUDcLC6ddjjnC5NlNXCRy6ZRlVzNxkJ0dij\njP/+5754BU/es5It37yGl79y1ZCvv3FRDnHRVho6+iiZlzW+mfBDQWos1S3d9DmlCksIYZAAMkYL\n8pIAOFjdNuxxDpcbq0Xx6Stnsenfr+HZz1/OzYtzmZkRz6J84xxKKZ/LzybE2Hj3kjwArpkfjAAS\nh9OtqWrplkZ0IQQgbSBjlhwbRV6yfcCMtUNxubV3ESbP4L6fvm8xvU633xMTfvm6ImZlxrMkP3ls\niQ6AZ8zLqcbOQQ34QoipSQLIOEhPiKG5q2/YY4YaP2GPsmKPsvr9Pnkpsdxz9eyA0jhWngDicEk3\nXiGEQaqwxkFKXBRNXb5HmIPRCyuc2w7yUs71DJOBhEIIkAAyLtLio2kZqQTiCu8pQOxRVrLMgY1S\nAhFCgASQcZEaFz1goOBQjKqf8P7vvnhGGiABRAhhCO87WohIjYumvceJY4iFnzxcbre3ET1cXbfA\n6P11aIQeZ0KIqUECyDhIizfW72gZph3E6Qr/SQivMcefnG3rCXJKhBChQHphjYOUOGNUeHNXn3cC\nxPM5I2Aa9JS4aD5XMpu52YGtsS6EiCwSQMaBZ1qR5mHaQcK9F5bHN2+cH+wkCCFCRHjXqYSI1H4l\nkKForXG4dEQEECGE8JAAMg5SzTaQZh9tIOZS5th8TFMihBDhSO5o48BTAvHVldfTOyvc20CEEKI/\nCSDjwB5lJTbK6nMwocssgkgVlhAikkgAGSdp8dE0+iiBOF2eACL/3UKIyCF3tHGSnhBNY4ePAOKW\nKiwhROSRADJOMhNivEvSns/plhKIECLyyB1tnGQkxPhc1lYa0YUQkSjsAohS6kal1FGlVLlS6lvB\nTo9HRqLRBuL29NntRxrRhRCRKKwCiFLKCjwI3AQsAD6slFoQ3FQZMhJicLk1Ld2Dx4I4PI3oMg5E\nCBFBwu2OdglQrrU+obXuA9YBq4OcJsAIIMCQ7SBSAhFCRKJwmwsrHzjT73klcGn/A5RSa4A1ANnZ\n2ZSWlgb8Zh0dHX6/vqrJBcCrW3ZQnT5wmdpTbca+I4cOEtd4NOD0jMVo8hLKIiUfIHkJVZIX/4Vb\nABmR1vph4GGA4uJiXVJSEvC5SktL8ff1BXUd/GzHJvJnz6dkWf6AfXvOtMCbW7lw6RJK5mcFnJ6x\nGE1eQlmk5AMkL6FK8uK/cKvCqgIK+z0vMLcFXaZZhTVUTyyXOQ5EVvITQkSScAsgO4EipdRMpVQ0\ncAewIchpAiAp1ka01ULDEIMJzzWiSwARQkSOsKrC0lo7lVJfBF4GrMAjWuuDQU4WAEopMhKiqWsf\nvFqfSwYSCiEiUFgFEACt9YvAi8FOx1CmpcdxsqFz0HYZSCiEiETyk3gczctOpKy2A60HDiY8N5mi\nBBAhROSQADKO5uYk0tHrpLp1YDWWzIUlhIhEckcbR/OyEwE4drZ9wHbPbLxRUoUlhIggEkDGUZEZ\nQI7WDgwgnkZ06cYrhIgkEkDGUXJsFLnJ9kElEE833iiZC0sIEUHkjjbOZmbEc7JxYE8sp0sGEgoh\nIo8EkHE2PT2O041dA7Z5G9GlDUQIEUEkgIyzaWnxNHb20dHr9G7zlECipBeWECKCyB1tnE1PjwPg\nVL9qLE8JxColECFEBJEAMs6mpRkBpH81lieASAlECBFJ5I42zrwlkKZ+AUQa0YUQEUgCyDhLtEeR\nFh89ZBWWDCQUQkQSCSATYHF+Mq8drqPHYaxE6HRprBaFUhJAhBCRQwLIBLjn6lnUtfeybsdpwCiB\nSPWVECLSSACZACtnpbMwL4mXDpwFjDaQKAkgQogIIwFkAiilWJCb5F0bREogQohIJAFkgszMjKeu\nvZeOXidOt1vmwRJCRBy5q02QWRnxAFQ0dOJ0aZnGRAgRcSSATJCZGQkAHK/vwOnWspiUECLiyF1t\ngkxPj0MpONnQidPllhKIECLi2IKdgEhlj7KSnxLLifpOXFoa0YUQkUdKIBNoRno8p5q6cLm0zIMl\nhIg4clebQIVpsVQ2deF0SxWWECLySACZQAWpcTR29tHW7cQmVVhCiAgjAWQCeaZ2P9nYiU3GgQgh\nIozc1SZQoRlA6tt7SYmNCnJqhBBifEkAmUCFqbHex5fNyQhiSoQQYvwFJYAopW5XSh1USrmVUsXn\n7fu2UqpcKXVUKfWufttvNLeVK6W+NfmpHr20+Gjioq0AXD1XAogQIrIEaxzIAeD9wO/7b1RKLQDu\nABYCecCrSqm55u4HgeuBSmCnUmqD1vrQ5CV59JRSFKbG0d7jYHZmQrCTI4QQ4yooAURrfRgYaoGl\n1cA6rXUvcFIpVQ5cYu4r11qfMF+3zjw2pAMIwL2rilBqyLwKIURYC7WR6PnAW/2eV5rbAM6ct/3S\noU6glFoDrAHIzs6mtLQ04MR0dHSM6fUA8ea/paVHx3SesRqPvISCSMkHSF5CleTFfxMWQJRSrwI5\nQ+z6jtZ6/US9r9b6YeBhgOLiYl1SUhLwuUpLSxnL60NJpOQlUvIBkpdQJXnx34QFEK31dQG8rAoo\n7Pe8wNzGMNuFEEIEQah1490A3KGUilFKzQSKgB3ATqBIKTVTKRWN0dC+IYjpFEKIKS8obSBKqfcB\nvwEygReUUnu01u/SWh9USj2F0TjuBL6gtXaZr/ki8DJgBR7RWh8MRtqFEEIYgtUL61ngWR/77gPu\nG2L7i8CLE5w0IYQQfgq1KiwhhBBhQgKIEEKIgEgAEUIIERCltQ52GiaMUqoeODWGU2QADeOUnGCL\nlLxESj5A8hKqJC8wXWudOdJBER1AxkoptUtrXTzykaEvUvISKfkAyUuokrz4T6qwhBBCBEQCiBBC\niIBIABnew8FOwDiKlLxESj5A8hKqJC9+kjYQIYQQAZESiBBCiIBIABlCOC6f259SqkIptV8ptUcp\ntcvclqaUekUpVWb+mxrsdA5FKfWIUqpOKXWg37Yh064Mvzav0z6l1PLgpXwwH3n5gVKqyrw2e5RS\nN/fbN+RyzqFAKVWolNqolDpkLkf9ZXN7WF2bYfIRdtdFKWVXSu1QSu018/JDc/tMpdR2M81PmhPQ\nYk5S+6S5fbtSasaYE6G1lr9+fxiTNR4HZgHRwF5gQbDTNco8VAAZ5237L+Bb5uNvAT8Pdjp9pP0q\nYDlwYKS0AzcDLwEKWAFsD3b6/cjLD4CvD3HsAvOzFgPMND+D1mDnoV/6coHl5uNE4JiZ5rC6NsPk\nI+yui/l/m2A+jgK2m//XTwF3mNsfAj5nPv488JD5+A7gybGmQUogg12CuXyu1roP8CyfG+5WA4+Z\njx8D3hvEtPiktd4MNJ232VfaVwOPa8NbQIpSKndyUjoyH3nxxbucs9b6JNB/Oeeg01rXaK3fMR+3\nA4cxVgsNq2szTD58CdnrYv7fdphPo8w/DVwL/N3cfv418VyrvwOr1BjX2pYAMlg+g5fPHe4DFoo0\n8C+l1NvmEr8A2VrrGvPxWSA7OEkLiK+0h+u1+qJZrfNIv6rEsMmLWfVxIcYv3rC9NuflA8Lwuiil\nrEqpPUAd8ApGCalFa+00D+mfXm9ezP2tQPpY3l8CSGS6Qmu9HLgJ+IJS6qr+O7VRhg3L7nfhnHbT\n74DZwDKgBvhlcJMzOkqpBOAZ4Cta67b++8Lp2gyRj7C8Llprl9Z6GcYqrZcA8yfz/SWADDbcsrph\nQWtdZf5bh7HuyiVAracKwfy3LngpHDVfaQ+7a6W1rjW/9G7gD5yrDgn5vCilojBuun/VWv/D3Bx2\n12aofITzdQHQWrcAG4GVGNWFnrWe+qfXmxdzfzLQOJb3lQAyWFgvn6uUildKJXoeAzcABzDycLd5\n2N3A+uCkMCC+0r4BuMvs8bMCaO1XnRKSzmsHeB/GtQHfyzmHBLOufC1wWGv9P/12hdW18ZWPcLwu\nSqlMpVSK+TgWuB6jTWcjcJt52PnXxHOtbgNeN0uNgQt2T4JQ/MPoQXIMoz7xO8FOzyjTPguj18he\n4KAn/Rh1na8BZcCrQFqw0+oj/U9gVCE4MOpvP+Ur7Ri9UB40r9N+oDjY6fcjL38207rP/ELn9jv+\nO2ZejgI3BTv95+XlCozqqX3AHvPv5nC7NsPkI+yuC7AE2G2m+QDwPXP7LIwgVw48DcSY2+3m83Jz\n/6yxpkFGogshhAiIVGEJIYQIiAQQIYQQAZEAIoQQIiASQIQQQgREAogQQoiA2EY+RAgxEqWUpzsr\nQA7gAurN511a68uCkjAhJpB04xVinCmlfgB0aK1/Eey0CDGRpApLiAmmlOow/y1RSm1SSq1XSp1Q\nSv1MKfVRc02H/Uqp2eZxmUqpZ5RSO82/y4ObAyGGJgFEiMm1FPgscAFwJzBXa30J8EfgS+YxvwLu\n11pfDHzA3CdEyJE2ENXQ3vwAAACnSURBVCEm105tzgmllDoO/Mvcvh+4xnx8HbCg31INSUqpBH1u\n7QchQoIEECEmV2+/x+5+z92c+z5agBVa657JTJgQoyVVWEKEnn9xrjoLpdSyIKZFCJ8kgAgReu4F\nis3V8Q5htJkIEXKkG68QQoiASAlECCFEQCSACCGECIgEECGEEAGRACKEECIgEkCEEEIERAKIEEKI\ngEgAEUIIERAJIEIIIQLy/wEFaEQPUdjDQwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "iBfpCbu6jsaB",
        "colab": {}
      },
      "source": [
        "def impulses(time, num_impulses, amplitude=1, seed=None):\n",
        "    rnd = np.random.RandomState(seed)\n",
        "    impulse_indices = rnd.randint(len(time), size=10)\n",
        "    series = np.zeros(len(time))\n",
        "    for index in impulse_indices:\n",
        "        series[index] += rnd.rand() * amplitude\n",
        "    return series    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BJ1kXWNLg_BD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "51dba178-72ff-48fc-d280-00ee7c2423fd"
      },
      "source": [
        "series = impulses(time, 10, seed=42)\n",
        "plot_series(time, series)\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9q+cZHx/v+r7t2L79dQBGnhihXh/r+nGyztkrVchZhYzQWc5tT+4DYOfOsdxfW7s5W7V5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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "uvMAqSatkcyX",
        "colab": {}
      },
      "source": [
        "def autocorrelation(source, φs):\n",
        "    ar = source.copy()\n",
        "    max_lag = len(φs)\n",
        "    for step, value in enumerate(source):\n",
        "        for lag, φ in φs.items():\n",
        "            if step - lag > 0:\n",
        "              ar[step] += φ * ar[step - lag]\n",
        "    return ar"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "iUv8l8nchJRZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "97676db8-78cc-4f13-dd5c-3e38b569164e"
      },
      "source": [
        "signal = impulses(time, 10, seed=42)\n",
        "series = autocorrelation(signal, {1: 0.99})\n",
        "plot_series(time, series)\n",
        "plt.plot(time, signal, \"k-\")\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r4YW1+2hp637o6HjhRkNzyBXTh5OW7ONv79Z23qfgCzt2V0wbTmaKn78sr+lx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\nUKgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "5_lx-AlWhT5v",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "9d359a3d-a00b-432d-b4be-d565d976febb"
      },
      "source": [
        "signal = impulses(time, 10, seed=42)\n",
        "series = autocorrelation(signal, {1: 0.70, 50: 0.2})\n",
        "plot_series(time, series)\n",
        "plt.plot(time, signal, \"k-\")\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FS51wOk9Nweuq9RLLotlNdPeP5L3QzW/pvBZ6htIc68l7H7Bckls8pxmAg92F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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "nWQ9fvFAOGRB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "eddd8f75-dc13-425c-d89c-2f7b93d3bb17"
      },
      "source": [
        "series_diff1 = series[1:] - series[:-1]\n",
        "plot_series(time[1:], series_diff1)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9gCtev5CmRUdxzuKjjqibuzbs4pM/f4J/faKfOdPq+dK7TuScxUdz8rxpR/xm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\nREQkMCUNEREJ7P8D3DhG9byNrLYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AvUI22RSONQd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "23dce7f5-2561-45d8-af44-2e33b7898d2b"
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "autocorrelation_plot(series)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f53e49d9860>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2XVPxxyUi/vaQ57onbakF+OMTSQnj9bsaqE5iRdh96vcByC57l9yy3q9jaska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\neVCOXRcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "ddRJGI1pic78",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        },
        "outputId": "3eed467f-64e9-4ccb-b3e0-756c94f6c3a8"
      },
      "source": [
        "from statsmodels.tsa.arima_model import ARIMA\n",
        "\n",
        "model = ARIMA(series, order=(5, 1, 0))\n",
        "model_fit = model.fit(disp=0)\n",
        "print(model_fit.summary())\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                             ARIMA Model Results                              \n",
            "==============================================================================\n",
            "Dep. Variable:                    D.y   No. Observations:                 1460\n",
            "Model:                 ARIMA(5, 1, 0)   Log Likelihood                2223.428\n",
            "Method:                       css-mle   S.D. of innovations              0.053\n",
            "Date:                Tue, 30 Jul 2019   AIC                          -4432.855\n",
            "Time:                        17:40:55   BIC                          -4395.852\n",
            "Sample:                             1   HQIC                         -4419.052\n",
            "                                                                              \n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          0.0003      0.001      0.384      0.701      -0.001       0.002\n",
            "ar.L1.D.y     -0.1235      0.026     -4.714      0.000      -0.175      -0.072\n",
            "ar.L2.D.y     -0.1254      0.029     -4.333      0.000      -0.182      -0.069\n",
            "ar.L3.D.y     -0.1089      0.029     -3.759      0.000      -0.166      -0.052\n",
            "ar.L4.D.y     -0.0914      0.029     -3.162      0.002      -0.148      -0.035\n",
            "ar.L5.D.y     -0.0774      0.029     -2.675      0.008      -0.134      -0.021\n",
            "                                    Roots                                    \n",
            "=============================================================================\n",
            "                  Real          Imaginary           Modulus         Frequency\n",
            "-----------------------------------------------------------------------------\n",
            "AR.1            1.0145           -1.1311j            1.5194           -0.1336\n",
            "AR.2            1.0145           +1.1311j            1.5194            0.1336\n",
            "AR.3           -1.8173           -0.0000j            1.8173           -0.5000\n",
            "AR.4           -0.6967           -1.6113j            1.7554           -0.3150\n",
            "AR.5           -0.6967           +1.6113j            1.7554            0.3150\n",
            "-----------------------------------------------------------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "A0l79ROF1xu1",
        "colab": {}
      },
      "source": [
        "df = pd.read_csv(\"sunspots.csv\", parse_dates=[\"Date\"], index_col=\"Date\")\n",
        "series = df[\"Monthly Mean Total Sunspot Number\"].asfreq(\"1M\")\n",
        "series.head()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "wVoq4cmx3-vk",
        "colab": {}
      },
      "source": [
        "series.plot(figsize=(12, 5))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "stmDLe8jEDQL",
        "colab": {}
      },
      "source": [
        "series[\"1995-01-01\":].plot()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "SXc9PkCXJd_a",
        "colab": {}
      },
      "source": [
        "series.diff(1).plot()\n",
        "plt.axis([0, 100, -50, 50])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "G1T-V7B8180O",
        "colab": {}
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "autocorrelation_plot(series)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "8jdIxEASH_1z",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "6eIY8wloG3Go",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:].diff(11 * 12)[11*12+1:])\n",
        "plt.axis([0, 500, -0.1, 0.1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "El2JSNZwG7UP",
        "colab": {}
      },
      "source": [
        "autocorrelation_plot(series.diff(1)[1:])\n",
        "plt.axis([0, 50, -0.1, 0.1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gvmZAKeAHACf",
        "colab": {}
      },
      "source": [
        "116.7 - 104.3"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "ReEbS1MpC50n",
        "colab": {}
      },
      "source": [
        "[series.autocorr(lag) for lag in range(1, 50)]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "7rdXm2UX3WsH",
        "colab": {}
      },
      "source": [
        "pd.read_csv(filepath_or_buffer, sep=',', delimiter=None, header='infer', names=None, index_col=None, usecols=None, squeeze=False, prefix=None, mangle_dupe_cols=True, dtype=None, engine=None, converters=None, true_values=None, false_values=None, skipinitialspace=False, skiprows=None, skipfooter=0, nrows=None, na_values=None, keep_default_na=True, na_filter=True, verbose=False, skip_blank_lines=True, parse_dates=False, infer_datetime_format=False, keep_date_col=False, date_parser=None, dayfirst=False, iterator=False, chunksize=None, compression='infer', thousands=None, decimal=b'.', lineterminator=None, quotechar='\"', quoting=0, doublequote=True, escapechar=None, comment=None, encoding=None, dialect=None, tupleize_cols=None, error_bad_lines=True, warn_bad_lines=True, delim_whitespace=False, low_memory=True, memory_map=False, float_precision=None)\n",
        "Read a comma-separated values (csv) file into DataFrame.\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "sYXNHu_trIH2",
        "colab": {}
      },
      "source": [
        "from pandas.plotting import autocorrelation_plot\n",
        "\n",
        "series_diff = series\n",
        "for lag in range(50):\n",
        "  series_diff = series_diff[1:] - series_diff[:-1]\n",
        "\n",
        "autocorrelation_plot(series_diff)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "s6SVHBpqrO1X",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "\n",
        "series_diff1 = pd.Series(series[1:] - series[:-1])\n",
        "autocorrs = [series_diff1.autocorr(lag) for lag in range(1, 60)]\n",
        "plt.plot(autocorrs)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}